Geodesic
Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde{G}_{2}$
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 483-508.

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Let $\Delta$ be thick affine building of type $\widetilde{G}_{2}$ the Laplace operators of $\Delta$; associated with a pair $(y_{1}, y_{2})$; is the Poisson transform of a suitable finitely additive measure on the maximal boundary $\Omega$ of $\Delta$; by using only the combinatorial structure of $\Delta$. 
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Mantero, A. M.; Zappa, A. Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde{G}_{2}$. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 483-508. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a12/

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